[Meta: please submit the direct link, not a link-shortened version]<p>This arXiv paper[1] is apparently from 2012. A good meta-resource and summary of attempts on P ?= NP, including this one, can be found at [2]. From [2]:<p>> Among all these papers, there is only a single paper that has appeared in a peer-reviewed journal, that has thoroughly been verified by the experts in the area, and whose correctness is accepted by the general research community: The paper by Mihalis Yannakakis. (And this paper does not settle the P-versus-NP question, but "just" shows that a certain approach to settling this question will never work out.)<p>[1] arXiv summary: <a href="http://arxiv.org/abs/1208.0954" rel="nofollow">http://arxiv.org/abs/1208.0954</a><p>[2] <a href="http://www.win.tue.nl/~gwoegi/P-versus-NP.htm" rel="nofollow">http://www.win.tue.nl/~gwoegi/P-versus-NP.htm</a>